Question 6:
A copper wire has diameter 0.5 mm and resistivity of 1.6 × 10−8 G m. What will
be the length of this wire to make its resistance 10 Ω? How much does the
resistance change if the diameter is doubled?
Answer:
Resistance (R) of a copper wire of length l and cross-section A is given by the
expression,
Diameter= 0.5 mm = 0.0005 m
Resistance, R = 10 Ω
Hence, length of the wire,
If the diameter of the wire is doubled, new diameter = 2 × 0.5 = 1 mm = 0.001 m
Therefore, resistance R’
Therefore, the length of the wire is 122.7 m and the new resistance is 2.5 Ω
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